Let f"(x)=4x^3 -2x and let f(x) have critical values -1, 0, and 1.?

Question

Let f"(x)=4x^3 -2x and let f(x) have critical values -1, 0, and 1. Determine which critical values give a relative maximum How do you figure this out and which is the right answer and why? a) -1 b) 0 c) 1 d) -1 and 1 e) none of these

Answer 1

Relative maximum means f''(x) < 0.

f''(-1) = -4+2 < 0

f''(0) = 0

f''(1) = 4-2 > 0

Answer: a) -1